Plotting points on a grid — including when the numbers go negative. Here's the full picture.
Your child is learning to describe the position of a point on a grid using two numbers, written as a pair in brackets: \((x, y)\). The first number tells you the horizontal position (left or right), and the second tells you the vertical position (up or down).
In the early years of primary school, your child worked with coordinates that were all positive — a grid that only covered the top-right area, with both numbers being 1, 2, 3, and so on. By Year 6 the grid has already expanded: the axes cross in the middle, creating four sections, and the numbers can be negative. At KS3 your child keeps working on that full grid.
This is a big step. It means a point can be to the left of the centre (negative x) or below the centre (negative y), or both. The grid now has four regions, called quadrants.
The two lines that form the grid are called axes. The horizontal one is the x-axis; the vertical one is the y-axis. The point where they cross — right in the middle — is called the origin, and its coordinates are \((0, 0)\).
This is the memory trick that every maths teacher uses, and it works brilliantly. To plot a point like \((3, 5)\):
The order matters. \((3, 5)\) and \((5, 3)\) are completely different points. The first number is always horizontal, the second is always vertical.
The four sections of the grid are numbered 1 to 4, going anticlockwise from the top-right:
| Quadrant | Signs | Position |
|---|---|---|
| 1 | (+, +) | Top-right |
| 2 | (-, +) | Top-left |
| 3 | (-, -) | Bottom-left |
| 4 | (+, -) | Bottom-right |
Your child doesn't need to memorise this table. Once they understand the signs (negative x = left, negative y = down), the quadrants follow naturally. But knowing they're numbered anticlockwise from the top-right can help in exam questions that reference quadrants by number.
Students also practise the reverse: looking at a point on a grid and writing down its coordinates. The process is the same in reverse — read across to the x-axis first, then read up or down to find the y value.
A common extension is to plot several points and join them to make a shape. "Plot (2, 1), (5, 1), (5, 4), and (2, 4). What shape have you made?" (A square, with sides of 3 units — and a square is also a rectangle, because all four of its angles are right angles.) This builds towards later work on transformations and straight-line graphs.
Plot the point \((-3, 4)\) on a coordinate grid.
Step 1: Start at the origin \((0, 0)\).
Step 2: The x-coordinate is \(-3\). Go 3 left along the x-axis (negative means left).
Step 3: The y-coordinate is \(4\). Go 4 up (positive means up).
Mark the point. It sits in quadrant 2 (top-left), because x is negative and y is positive.
Without plotting, can you work out which quadrant each point falls in?
Once your child can do this without a grid, they've really understood how the sign of each coordinate maps to position.
A good challenge to finish: "I'm thinking of a point in quadrant 2. What do you know about it?" (Answer: the x-coordinate must be negative and the y-coordinate must be positive.) This kind of reasoning question is exactly what schools are building towards.
Our Four Quadrant Explorer lets your child practise plotting and reading coordinates across all four quadrants. It's free, works on any device, and there's no sign-up needed.
Play Four Quadrant Explorer on MaffsGamesMaffsGames needs no account and no sign-up; what it records while your child plays is set out on the privacy page.